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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Berezin’s quantization on flag manifolds and spherical modules

Author: Alexander V. Karabegov
Journal: Trans. Amer. Math. Soc. 350 (1998), 1467-1479
MSC (1991): Primary 58F06; Secondary 22E47
MathSciNet review: 1458307
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Abstract: We show that the theory of spherical Harish-Chandra modules naturally gives rise to Berezin’s symbol quantization on generalized flag manifolds. It provides constructions of symbol algebras and of their representations for covariant and contravariant symbols, and also for symbols which so far have no explicit definition. For all these symbol algebras we give a general proof of the correspondence principle.

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Alexander V. Karabegov
Affiliation: LCTA, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia

Keywords: Quantization, symbols, Harish-Chandra modules
Received by editor(s): December 14, 1994
Received by editor(s) in revised form: June 14, 1996
Article copyright: © Copyright 1998 American Mathematical Society